arXiv:2505. 04346v2 Announce Type: replace Abstract: Clustering aims at partitioning data points into groups of similar objects without knowing about the class labels.
Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.
arXiv:2512.23348v3 Announce Type: replace-cross Abstract: We introduce a data-analysis framework based on filtrations of finite topological spaces. Starting from a finite metric data set, we construc...
arXiv:2512. 16558v3 Announce Type: replace Abstract: Clustering is a cornerstone of modern data analysis.
arXiv:2606. 06342v1 Announce Type: cross Abstract: Topological Data Analysis (TDA) offers a principled, intrinsic lens for comparing neural representations.
arXiv:2606. 28268v1 Announce Type: cross Abstract: Test-time adaptation (TTA) has emerged as a promising paradigm for mitigating distribution shifts in deep models.
The article introduces a new non‑archimedean metric, the cophenetic metric, defined on persistent homology classes of all degrees. It demonstrates that zeroth persistent homology combined with this metric and various hierarchical clustering algorithms yields statistically verifiable, commensurate topological information on multiple datasets. The resulting clusters, evaluated by silhouette score and Rand index, perform well, and the metric enables visualization of inter‑relations among persistent homology classes across all degrees via rooted trees.
arXiv:2601. 21207v4 Announce Type: replace-cross Abstract: Combinatorial and topological structures, such as graphs, simplicial complexes, and cell complexes, form the foundation of geometric and topological deep learning (GDL and TDL) architectures.